A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion

2009 ◽  
Vol 44 (5) ◽  
pp. 1103-1124 ◽  
Author(s):  
Miloš Kopa ◽  
Thierry Post
Keyword(s):  
Stochastic Dominance ◽  
New Approach ◽  
First Order ◽  
Value Stocks ◽  
Order Stochastic Dominance ◽  
Market Portfolio ◽  
The Face ◽  
Binary Choices ◽  
Return Distributions ◽  
Optimality Test

AbstractExisting approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance-based procedures promise a useful nonparametric alternative. However, these procedures have been limited to considering binary choices. In this paper we take a new approach that considers all diversified portfolios and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. Using our new test, we show that the U.S. stock market portfolio is significantly FSD nonoptimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no nonsatiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.

scholarly journals The concept of stochastic dominance in ranking investment alternatives

2005 ◽  
Vol 50 (164) ◽  
pp. 135-149
Author(s):  
Dejan Trifunovic
Keyword(s):  
Stochastic Dominance ◽  
Distribution Functions ◽  
Third Order ◽  
Ranking Problem ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Arbitrage Opportunities ◽  
Second Order Stochastic Dominance ◽  
Mean Variance ◽  
Almost Stochastic Dominance

In order to rank investments under uncertainty, the most widely used method is mean variance analysis. Stochastic dominance is an alternative concept which ranks investments by using the whole distribution function. There exist three models: first-order stochastic dominance is used when the distribution functions do not intersect, second-order stochastic dominance is applied to situations where the distribution functions intersect only once, while third-order stochastic dominance solves the ranking problem in the case of double intersection. Almost stochastic dominance is a special model. Finally we show that the existence of arbitrage opportunities implies the existence of stochastic dominance, while the reverse does not hold.

SAMPLING ERROR IN FIRST ORDER STOCHASTIC DOMINANCE

1987 ◽  
Vol 10 (3) ◽  
pp. 259-268 ◽  
Author(s):  
William E. Stein ◽  
Roger C. Pfaffenberger ◽  
Dan W. French
Keyword(s):  
Stochastic Dominance ◽  
Sampling Error ◽  
First Order ◽  
Order Stochastic Dominance

scholarly journals On the existence of certainty equivalents of various relevant types

2003 ◽  
Vol 2003 (9) ◽  
pp. 447-458 ◽  
Author(s):  
J. C. R. Alcantud ◽  
G. Bosi
Keyword(s):  
Stochastic Dominance ◽  
Cooperative Games ◽  
Risk Attitudes ◽  
Translation Invariance ◽  
Certainty Equivalence ◽  
First Order ◽  
Certainty Equivalents ◽  
Order Stochastic Dominance ◽  
Positive Homogeneity ◽  
General Conditions

We tackle the problem of associating certainty equivalents with preferences over stochastic situations, which arises in a number of different fields (e.g., the theory of risk attitudes or the analysis of stochastic cooperative games). We study the possibility of endowing such preferences with certainty equivalence functionals that satisfy relevant requirements (such as positive homogeneity, translation invariance, monotonicity with respect to first-order stochastic dominance, and subadditivity). Uniqueness of the functional is also addressed in fairly general conditions.

scholarly journals Second-Order Stochastic Dominance, Reward-Risk Portfolio Selection, and the CAPM

2008 ◽  
Vol 43 (2) ◽  
pp. 525-546 ◽  
Author(s):  
Enrico De Giorgi ◽  
Thierry Post
Keyword(s):  
Stock Returns ◽  
Portfolio Selection ◽  
Stochastic Dominance ◽  
Risk Model ◽  
Second Order ◽  
Order Stochastic Dominance ◽  
Market Portfolio ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Mean Variance

AbstractStarting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

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